Atrisiniet 2x^2+cx^2+7x+60=0

$$2 x ^ { 2 } + c x ^ { 2 } + 7 x + 60 = 0$$

Atrast c

$$c=-2-\frac{7}{x}-\frac{60}{x^{2}}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

Atņemiet 2x^{2} no abām pusēm. Atņemot nu nulles jebko, iegūst tā noliegumu.

$$cx^{2}+7x+60=-2x^{2}$$

Atņemiet 7x no abām pusēm.

$$cx^{2}+60=-2x^{2}-7x$$

Atņemiet 60 no abām pusēm.

$$cx^{2}=-2x^{2}-7x-60$$

Vienādojums ir standarta formā.

$$x^{2}c=-2x^{2}-7x-60$$

Daliet abas puses ar x^{2}.

$$\frac{x^{2}c}{x^{2}}=\frac{-2x^{2}-7x-60}{x^{2}}$$

Dalīšana ar x^{2} atsauc reizināšanu ar x^{2}.

$$c=\frac{-2x^{2}-7x-60}{x^{2}}$$

Daliet -2x^{2}-7x-60 ar x^{2}.

$$c=-2-\frac{7x+60}{x^{2}}$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\text{ and }c\leq -\frac{431}{240}\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right,$$